A Palm can be set up to handle mail in both offline and online modes. In offline mode, mail is received and sent at the desktop, but can be viewed and edited on the Palm. Upon syncing, pending mail on the Palm is sent and new mail on the desktop is copied to the Palm.
Palms are also capable of recieving and sending mail themselves. All that's needed is a connection to the network, whether via Ethernet, 802.11, Bluetooth, or even through a cellular/PCS network.